In what order are chained implications evaluated? (i.e. $a \implies b \implies c$)

Question

Implication does not appear to be associative:

a  b  c | (a -> b) -> c | a -> (b -> c)
F  T  F | F             | T
F  F  F | F             | T

Is $a \implies b \implies c$ evaluated as $a \implies (b \implies c)$ or $(a \implies b) \implies c$?

Answer 1

In computer science, the convention that $a \to b \to c$ means $a \to (b\to c)$ is near universal -- because, through the Curry-Howard isomorphism, such formulas correspond to useful curried types in functional languages.

Answer 2

The usual convention associates to the right, so $a \rightarrow b \rightarrow c$ is the same as $(a \land b) \rightarrow c$. But it's much better to put parentheses around.

Answer 3

It really depends on the author, of course.

That said, Carl Mummert, who researches in mathematical logic, indicates that he uses a->b->c to mean (a->(b->c)) in a comment in another thread. So, as others have kindly pointed out, if you're reading a logic text, I'd think it probable that you'd encounter that convention more often than anything else.